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Page 249
... orthogonal if ( x , y ) = 0. Two manifolds M , N in H are orthogonal manifolds if ( M , N ) = 0. We write xy to indicate that x and y are orthogonal , and MN to indicate that M and N are orthogonal . The orthocom- plement of a set AC is ...
... orthogonal if ( x , y ) = 0. Two manifolds M , N in H are orthogonal manifolds if ( M , N ) = 0. We write xy to indicate that x and y are orthogonal , and MN to indicate that M and N are orthogonal . The orthocom- plement of a set AC is ...
Page 251
... orthogonal projection . It is the uniquely determined orthogonal projection with ES = M. For if D is an orthogonal projection with DSM then ED = D and , since ( I - D ) CH M , we see that E ( I - D ) 0. Thus = = D = ED + E ( I – D ) = E ...
... orthogonal projection . It is the uniquely determined orthogonal projection with ES = M. For if D is an orthogonal projection with DSM then ED = D and , since ( I - D ) CH M , we see that E ( I - D ) 0. Thus = = D = ED + E ( I – D ) = E ...
Page 357
... Orthogonal Series and Analytic Functions The following set of exercises is concerned with the application of linear space methods to the theory of orthogonal series . The most important special case of this theory is that of Fourier ...
... Orthogonal Series and Analytic Functions The following set of exercises is concerned with the application of linear space methods to the theory of orthogonal series . The most important special case of this theory is that of Fourier ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ